Comment by amelius

Thanks but I was thinking more about how fields drop off in 2D space versus 3D space. Simple electrostatic example: consider a 1D string of identical resistors. Voltage drops linearly as you go along this string. Now consider a 2D grid of resistors: voltage does not change linearly anymore if you move between two points (current will move in a more complicated spread-out pattern). So the dimensionality changes how fields behave.